Question

a bar of solid circular cross section is loaded in tension by forces p. the bar has length l=16in and diameter 0.50in. the material is a magnessium alloy having modulus of elasticity E=6.4*10^6 psi. the allowable stress in tension is epsillon allow=17000psi and the elongation of the bar must not exceed 0.04 in. what is the allowable value of the forces p?

Answer 1

Answer:3142 Pound force

Explanation:

Given

Length(L)=16 in.

diameter=0.5 in.

Modulus of elasticity (E)$=6.4\times 10^6 psi.$

Allowable stress $\left ( \sigma _{allowable}\right )=17000 psi$

Max elongation of the bar =0.04 in.

Also we Know

Elongation is given

$\Delta L=\frac{PL}{AE}$

where

P=Force applied

L=length of bar

A=Cross-section

E=Modulus of Elasticity

$A=\frac{\pi d^2}{4}=\frac{\pi}{16} in.^2$

$0.04=\frac{P\times 16\times 16}{\pi \times 6.4\times 10^6}$

$P=3142 pound\ force\approx 13.976 kN$

corresponding stress is $\frac{3142}{\frac{\pi }{16}}=16,000 psi$

Which is less than Allowable stress

thus allowable value of Force P is 3142 Pound force or 13.976 kN